Consider the following initial-value problem. -1 -2 X' = + X(0) = (:)- Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue. K1 K2 Solve the initial-value problem. X(t) =

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
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Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 80E
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Consider the following initial-value problem.
(;小)
-1 -2
X' =
X(0) =
+
(:)-
Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.)
=
Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.
K1
K, =
Solve the initial-value problem.
X(t) =
Transcribed Image Text:Consider the following initial-value problem. (;小) -1 -2 X' = X(0) = + (:)- Find the eigenvalues of the coefficient matrix A(t). (Enter your answers as a comma-separated list.) = Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue. K1 K, = Solve the initial-value problem. X(t) =
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